2001 AMC 8 第 22 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
22.
在一场二十道题的测试中，每答对一题得 分，未作答一题得 分，答错一题得 分。下列哪个分数不可能出现？
On a twenty-question test, each correct answer is worth points, each unanswered question is worth point and each incorrect answer is worth points. Which of the following scores is NOT possible?
答案：E
小提示：
检查接近 的分数
Check scores near
大提示：
若答对 题，只可能得到两个分数
With correct answers, only two scores are possible
解答：
答对 题时，分数是 。
答对 题时，根据剩下一题是答错还是未作答，分数是 或 。
答对 题时，剩下两题可以贡献 、 或 分，所以可得 、 或 。
因此列出的分数 都可能，而 不可能。
所以正确答案是 E。
With correct answers, the score is .
With correct answers, the score is either or , depending on whether the remaining question is incorrect or unanswered.
With correct answers, the remaining two questions can contribute , , or points, giving , , or .
Thus the listed scores are possible, while is not.
Thus, E is the correct answer.
其他年份的第 22 题
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